Question

# The number 5149+5148+5147+...+51+1 is divisible by

A
10
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B
20
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C
25
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D
50
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Solution

## The correct options are A 10 B 50 C 20 D 251+51+512...+5149=5150−151−1=5150−150Hence it is divisible by 2,5,10,25 and 50.To check if the number is divisible by 20, we need to check the last two digits of the sum.We can observe that, the last two digits of the odd powers of 51 are 51, while those of the even powers are 01. Hence, the last two digits of the sum of the series will be equal to the last two digits of 25(51+01)=1300 which is 00. Hence, the sum is also divisible by 20. Hence, all the options are correct.

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